where \(g_*(T)\)  is the number of relativistic degrees of freedom (which depends on temperature), and \(\gamma \)  parametrizes the ratio between the PBH mass and the mass of the collapsing horizon-sized region at PBH formation, which typically takes values \(\gamma \in [0.2,\,1]\) . In the following, we fix \(\gamma =0.8\)  and use the numerical results of Ref. [1]} for \(\delta _c(w)\) .
